Pythagoras

The significance of Pythagorean ideas

Introduction

Best known today for the so-called Pythagorean theorem, the sixth-century
BC Greek mystic and philosopher Pythagoras taught far more than geometry
at the school, or ashram, he founded in Kroton, Italy. Widely
traveled throughout Asia Minor as well as in ancient Egypt, Babylon,
Persia and India, Pythagoras absorbed the sacred knowledge of the ancient
world, and re-cast it in a form that would form the basis for modern
science, philosophy, mathematics, and music theory. Upon his return
to Greece, Pythagoras formed a spiritual brotherhood devoted to social
equality, a vegetarian lifestyle, and the study of sacred teachings
as a form of Yoga, to refine the mind and the soul in order to avoid
re-incarnation, or the cycle of rebirth. The central concept of Pythagoras’ teachings,
was harmonia, the Divine Harmony at the core of both cosmos and psyche, a
concept derived from the religious tradition of Orpheus, but
which was to lead to the teachings of Plato, and later to both the seven
liberal arts of medieval education, the trivium and the quadrivium, and,
eventually, to the development of empirical science in the seventeenth
century. Now, as Buckminster Fuller states: “To be positive about
the future you have to know a great deal.” Perhaps the knowledge
required is re-integrated world-view based on the Pythagorean integration
of the subjective and objective, Eastern and Western, branches of knowledge,
which may once again point the way to a successful future.

The sixth century scene evokes the image of an orchestra expectantly
tuning up, each player absorbed in his own instrument only, deaf to the
caterwaulings of the others. Then there is a dramatic silence, the conductor
enters the stage, raps three times with his baton, and harmony emerges
from the chaos. The maestro is Pythagoras of Samos, whose influence on
the ideas, and thereby on the destiny, of the human race was probably
greater than that of any single man before or after him.

Pythagoras defies categorization: a primary thinker in philosophy, mathematics,
music and cosmology, he may in fact be best thought of as one who challenges
the legitimacy of categories. Anyone who conceives of Pythagoras as the
inventor of a geometric theorem, the formulator of laws of music theory,
and the utterer of cryptic aphorisms will miss the essence of his thought
entirely, for the whole point of what he taught is the interrelatedness
of all human knowledge.

--Jamie
James, The Music of the Spheres: Music, Science, and the Natural Order
of the Universe (New York: Grove Press, 1993), p. 23.

Pythagoras is sometimes described in histories of
philosophy as a man who had two separate interests-a religious reformer,
who taught the doctrine of transmigration and instituted a cult society,
and a man of science who did much to lay the foundations of mathematics,
that is to say of arithmetic, geometry, astronomy and music. Transmigration
was, until very recent times, regarded by most modern Europeans as
a rather crude and barbaric form of the doctrine of immortality. Also,
it is not at once obvious to our minds that there is any connection
between the immortality of the soul and mathematics. So the historian
was disposed to dismiss the religious Pythagoras with brief and apologetic
notice, and to concentrate on the scientific Pythagoras and his mathematical
doctrine that the essential reality of things is to be found in numbers.
But that is not the way to understand a great philosopher’s apprehension of the world.
The vision of philosophic genius is a unitary vision. Such a man does
not keep his thought in two separate compartments, one for weekdays the
other for Sundays. We begin to understand Pythagoras when we see that
the two sides of his philosophy meet in the conception of harmony-a conception
that has a meaning both in the spiritual and the physical world. And
the germ of this philosophy was a discovery in the field, not of arithmetic
or geometry, but of music.

--F.M.
Cornford, Before and After Socrates (Cambridge: Cambridge University
Press, 1966), pp. 65-66.

If you listen to Werner Heisenberg lecturing about
Pythagoreanism in his own work on the quantum theory, you will hear
him emphasize that the basic building blocks of nature are number and
pattern, that the universe is not made out of matter but out of music. The
historians of science I worked with in the University regarded Pythagoras
as a magician, a shamanistic madman from the cults of the Near East;
Yet both Whitehead and Heisenberg regarded him as a genius of the highest
order who laid the foundation upon which our entire Western civilization
is based.

Pythagoras is said to have taught that the mathematical entities,
such as numbers and shapes, were the ultimate stuff out of which the real
entities of our perceptual experience are constructed. As thus baldly stated,
the idea seems crude, and indeed silly. But undoubtedly, he had hit upon a
philosophical notion of considerable importance; a notion which has a long
history, and which has moved the minds of men, and has even entered into Christian
theology. About a thousand years separate the Athanasian Creed from Pythagoras,
and about two thousand four hundred years separate Pythagoras from Hegel.
Yet for all these distances in time, the importance of definite number in
the constitution of the Divine Nature, and the concept of the real world as
exhibiting the evolution of an idea, can both be traced back to the train
of thought set going by Pythagoras.

--Alfred North Whitehead, Science and the Modern World (Cambridge: Cambridge
University Press, 1928), pp. 27-28.

None of Pythagoras' own work has survived, but the ideas fathered on him
by his followers would be among the most potent in modern history. Pure
knowledge, the Pythagoreans argued, was the purification (catharsis) of
the soul. This meant rising above the data of the human senses. The pure
essential reality, they said was found only in the realm of numbers. The
simple, wonderful proportion of numbers would explain the harmonies of music
which were the beauty of the ear. For that reason they introduced the musical
terminology of the octave, the fourth, the fifth, expressed as 2:1, 3:1
and 4:3.

Pythagorean doctrine was all-inclusive in its intention and all-permeative
in actual effect, and in some fields it retained its potency until well
into the modern period. The notion of cosmic order and its corollaries,
perhaps better known as universal harmony, stemmed from the school of Pythagoras
in the sixth century B.C. It flourished throughout the classical period
(most notably in the Academy of Plato and in the Roman circle of Neoplatonists
around Plotinus), cross-pollinated with Stoics and Peripatetics, scattered
seed as far abroad as the Hermeticists and the Cabalists and the Syrian
syncretists and St. Augustine, and came to full bloom in the renaissance.
. . Pythagorean cosmology, though withered, did not die until the acceptance
of Newtonian science and Humian philosophy. . . In the meantime, however,
the cosmic order first propounded by Pythagoras had provided the stimulus
and the cohesion for the best Western thought through all the intervening
centuries. And it must be mastered, I believe, if we wish to comprehend
the art of those centuries.

. . . the Pythagoreans transformed the Orphic mystery
cult into a religion which considered mathematical and astronomical studies
as the main forms of divine worship and prayer. The physical intoxication
which had accompanied the Bacchic rites was superseded by the mental
intoxication derived from philo-sophia, the love of knowledge.It was one of the many key concepts they coined and which are still basic
units in our verbal currency. . . .'Pure science' is
another of their coinages; it signified not merely a contrast to the
'applied' sciences, but also that the contemplation of the new mysteria
was regarded as a means of purifying the soul by its immersion in the
eternal. Finally, 'theorizing' comes from Theoria, again a word
of Orphic origin, meaning a state of fervent contemplation and participation
in the sacred rites (thea spectacle, theoris spectator,
audience).

Contemplation of the 'divine dance of numbers' which held
both the secrets of music and of the celestial motions became the link
in the mystic union between human thought and the anima mundi.
Its perfect symbol was the Harmony of the Spheres-the Pythagorean Scale,
whose musical intervals corresponded to the intervals between the planetary
orbits; it went reverberating through 'soft stillness and the night'
right into the poetry of the Elizabethans, and into the astronomy of
Kepler.

It was indeed this sublimated form of Orphic mysticism which, through
the Pythagorean revival in Renaissance Italy, inspired the Scientific
Revolution. Galileo, Descartes, and Newton all regarded God as a kind
of 'chief mathematician of the universe. Geometry existed before the
Creation, is co-eternal with the mind of God, is God himself', wrote
Kepler; and the other giants echoed his conviction. The 'oceanic feeling'
of religious mysticism had been distilled into differential equations;
the mind of the anima mundi was reflected in the rainbow colours
of the spectroscope, the ghostly spirals of distant galaxies, the harmonious
patterns of iron-filings around a magnet.

Everyone finds a tremendous appeal in music because music
arises from so fundamental a source that it is parallel to the structure
of life and to that of the cosmos as a whole. This is why Pythagoras
wrote that music and the universe of heavenly bodies are governed by
the same mathematical laws. It is also why music has the power to resonate
with every level of the awareness of the listener - mind, intellect,
emotions and pure creative intelligence.